Hollywood's female actors tend to fall into one of two categories when talking about themselves. The sexy starlet types will try effusively to convince you they were tomboys growing up, while the serious actors – irritated to be talking about anything but the art - will begrudgingly allow you to write that they were dark-minded toddlers or troubled teens. So, Rooney Mara: which were you?

"I like that. That's good." She smiles, and it takes her extraordinarily malleable face from blank to beautiful in an instant. "Well, OK: when I was three or four, I decided to dress up for Halloween as Clara, the crippled girl in the Heidi books. I wanted to make it authentic so I insisted my mom wheel me around in a buggy; you know, because the crippled girl needed a wheelchair."

Did she agree to that? "Sure she did. She was totally on board."

Certainly, then, one couldn't accuse Rooney Mara of lacking the requisite, natural-born imagination from which to draw the range of characters she's created, from her blistering tour de force as Lisbeth Salander in David Fincher's version of The Girl With The Dragon Tattoo, to her short but memorable turn as Mark Zuckerberg's quietly furious girlfriend at the start of The Social Network. But it's her face, sculpted in the tradition of a Mary Pickford or Mae Marsh – all Slavic cheekbones, porcelain skin and cool, intelligent eyes – that instantly mesmerises. It's an extraordinary face: plain and pretty at the same time, she gives away nothing in person but everything when in front of the camera. Steven Soderbergh, director of her latest film Side Effects, describes it as "[a] very classical, almost silent-movie face; very 'shootable'."

Her overly guarded demeanour, too, has drawn as much comment as her work. Warnings from colleagues about Mara the interviewee ranged from the semi-flattering ("impenetrable") to the cautionary ("tricky") to the bluntly unflattering ("miserable as fuck"). She's used to the question, and readily addresses it: "I feel like I've been guarded since I was about three years old. I don't know why. I come from such a huge family, so maybe it's that. Maybe it comes from going to Christmas and having 30 people all in your face at once. I've always been a bit like, 'Aaargh!'" Including at family photos? "Yeah, exactly. Like, 'What am I smiling on demand for? This is so weird.'"

What of her burgeoning reputation as the Greta Garbo of her generation? She laughs. "Oh God, I don't know. I don't find myself intriguing. Does anyone? I live with myself. I think maybe people find me difficult to read. It's a hard question. I'll tell you one thing about my face, though: I am a horrible liar. So even though people find me to be mysterious and intriguing, trust me, if I don't like something you say, you'll read it on my face."

'I learn a lot from Jude Law when we do interviews together … Jude is very generous with his answers and I feel like he gave me the space to be more open the next time'

Mara, it is clear, doesn't suffer fools, possibly a byproduct of growing up in a huge Irish-Italian brood ("Think every stereotype in existence!"). The family has an impressive NFL lineage (she's the great granddaughter of New York Giants founder Tim Mara and Pittsburgh Steelers founder Art Rooney Sr), while sister Kate Mara is also an actor. During a dual interview yesterday with Side Effects co-star Jude Law, she was asked what it was like to kiss Catherine Zeta-Jones on screen, and her internal eye roll was barely contained. (Her answer was the adorably teenage, "I don't know. Fine. Nice. Whatever", but the sentiment could easily have been, "Come on, don't be a dick.") A few minutes later she was asked a very specific question about her pay cheque. "That was totally weird, right?" she asks me the next day, in innocent disbelief at the intrusive question. "I wanted to ask, 'Why, did you bring a calculator?' But he was so mad that I didn't answer."

Disingenuousness, stupidity, the trite and the obvious: all are anathema to Mara's nature. A steely shyness prevents her from talking freely like Law, at whom she gazes in awe as he spews quotable lines with the easy smile of a publicity mill veteran who knows how to work the system. "I learn a lot from Jude when we do interviews together," she admits. "Alone, I am still pretty guarded but Jude is very generous with his answers and I feel like he gave me the space to be more open the next time."

She's currently doing the rounds in Berlin, promoting Soderbergh's Side Effects. In a recent article, Soderbergh was quoted as saying that Mara "didn't want to be friends with me, she just wanted to get on with the job". She looks slightly indignant. "Yeah, I read that!" she says, jokingly annoyed. "I was like, 'What the fuck is he talking about?' In fact, the reason I am talking a bit funny right now is because I was hanging out with Steven last night – because we are friends! – and he gave me scalding French fries and I burned my mouth. He's so dry and tongue in cheek, sometimes it's hard to tell if he's serious or joking." I confirm this later, reading an entertaining exchange between Mara and Soderbergh in Interview, in which Mara, guard down, professes to love the word "cunt", and cheerfully tells the Oscar-winning director he is "super-immature".

Side Effects is Soderbergh's silver-screen swansong (he's retiring from film directing to concentrate on other projects). A clever mix of classic thriller and cultural introspection – about, in this case, the pharmaceutical industry – it's another deft genre-blend from a man who defies categorisation. You can see why he'd cast Mara as Emily, a troubled woman who may or may not be as she seems. Mara offers a layered performance as the depressed, sporadically sexualised Emily, her face as expressive as it was playing the heavily pierced, creepily coiffed Salander.

As with Kristen Stewart and Jennifer Lawrence for Twilight and The Hunger Games respectively, there must have been pressure to make good on a role so beloved by millions when she stepped into Salander's spiked biker boots. "I had my own protectiveness of the character the same way every other fan has," she argues. "You can't think about that many million people when you're doing a job." Pressed about how she prepares for such a role, Mara grows prickly. "Nothing all that interesting," she deflects. "I mean, I read a lot. Interesting to me but nothing I could ... nothing specific I care to label. When I did Dragon Tattoo, I didn't have a single interview where I wasn't asked about the process. I had to learn so many extreme things, but it distils the whole experience down to a list of things including 'I cut my hair' and 'I learned to ride a bike'. It isn't that important."

'The next big thing thing happens all the time. I guess I don't really measure myself by what others think'

Lisbeth my dear: Mara in The Girl With The Dragon Tattoo. Photograph: Alamy

There's something a young actor in couture talking about the "art" that could be truly grating, but Mara is genuine in her earnestness. It's that earnestness, coupled with a truly chameleon-like gift to climb into the skin of a character, that make her plea to keep sealed the magician's cloth seem more naive than pretentious. She was a total unknown when she ran the gauntlet of Johansson, Portman and Mulligan to win the role of Salander. And she knows how lucky she is to find herself working on films such as Spike Jonze's sci-fi romance Her, or Terrence Malick's "Untitled Film". She's recently been pictured horsing around on set with Ryan Gosling, and says of Malick, "I want to work with people who are uncompromising, and Terry is one of those people."

That's a pretty impressive list of directors for a girl whose body of work pre-Dragon Tattoo was a bunch of unheard-of films and an episode of Law & Order: SVU, but Hollywood's habit of taking a promising actor and elevating them to It Girl status beyond the capacity of their embryonic CV is not lost on Mara.

"The 'next big thing' thing happens all the time," she agrees. "I guess I don't really measure myself by what others think. So even though I have gotten to work with some amazing directors and you might perceive me to be that girl, that isn't how I see myself. So if one day nobody wants to work with me it won't be this massive surprise."

What would she do if that were actually to happen? "I'd like to flip houses," she says, her eyes lighting up brighter than any movie talk so far. "I'm absolutely not buying an apartment. But I go to a lot of open houses." She gives the most ladylike of dirty laughs: "I like to go and watch."

The actor has long had a fraught relationship with the media and their intrusions on his private life. As he promotes his new film with Steven Soderbergh, he talks to Stuart Jeffries about life post-Leveson and his love of theatre